U8D9 pencil, highlighter, red pen, calculator, notebook Have out: Bellwork: 1. If the given point is on the terminal side of  (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) a. b. c. 2. Draw a sketch of . Then find THREE angles that are coterminal with .   total:

Bellwork: 1. If the given point is on the terminal side of  (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) Bellwork: a. The reference Δ is an isosceles right Δ. Therefore, It is a Δ. (45˚–45˚–90˚ Δ) y x +1 θ +2 +1 α 1 +1 +2 total:

The reference Δ is a 30˚–60˚–90˚ Δ. Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) The reference Δ is a 30˚–60˚–90˚ Δ. b) In radians, it is a Δ. y x ½ is the smallest side, so it must be opposite from the smallest angle, 30˚. θ must be across from α = 60˚. α +2 1 +1 +1 +1 +2

Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) c) (1, 0) y x +1 +2 1 total:

2. Draw a sketch of θ. Then find THREE angles that are coterminal with θ.   –72˚ + 360 +1 288o +1 θ x x θ +1 +1 –72˚ – 360 +1 –432o +1 +1 +1 648o or –792o or ? or or ? total:

Introduction to Trig Equations Recall from previous lessons which trig functions are positive in each quadrant: Remember: All Students Take Calculus y x II III IV I y x sin all tan cos When we say 0 ≤ θ < 2π, we are considering ONE full rotation of the circle.

Introduction to Trig Equations Example #1: Solve cos θ = for 0 ≤ θ < 2π. cos θ > 0 in quadrants ___ and ___. I IV QI Draw a sketch of θ for the ____ solution. y x Label the sides of the reference triangle. 30–60–90 Hint: It’s a ____________ triangle.  θ = 30°

This is the SAME reference triangle as in Q1, just rotated. Therefore: Example #1: Solve cos θ = for 0 ≤ θ < 2π. QIV Draw a sketch of θ and α for the ____ solution. y x Label the sides of the reference triangle. This is the SAME reference triangle as in Q1, just rotated. Therefore:  α Therefore, if we only know cos θ = for 0 ≤ θ < 2π, then there are 2 solutions: and

Example #2: Solve cos θ = for 0 ≤ θ < 2π. cos θ < 0 in quadrants ___ and ___. II III y x QII y x   α α QIII

Work on the Practice. Example #3: Solve sin θ = 0 for 0 ≤ θ < 2π. Since sin θ = ___ and r > ___, then sin θ = 0 means y = ___. Where on a coordinate plane is y = ___? x–axis y x Work on the Practice.

cos θ < 0 in quadrants II and III. Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. cos θ < 0 in quadrants II and III. a) y x QII y x   α α QIII

sin θ < 0 in quadrants III and IV. Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. sin θ < 0 in quadrants III and IV. b) y x y x   α α QIII QIV

tan θ < 0 in quadrants II and IV. Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. c) tan θ < 0 in quadrants II and IV. QII y x y x   α α QIV

Quiz Time After the quiz, work on the rest of the worksheet. Clear your desk except for a pencil, highlighter, and a calculator! After the quiz, work on the rest of the worksheet.

Finish the practice worksheets